The number of dynamics needed to model the motion between a Chief and Deputy satellites has grown greatly since the introduction of the Hill, Clohessy-Wilshire (HCW) equations of motion were introduced. The models have grown to include various things like perturbations, specifically drag, J2, and solar radiation pressure. Dynamics models have also been developed that use True Anomaly as the independent variable instead of time. A lot of work has been put forth to also include cases where the Chief is in an eccentric orbit. While these models have increased the fidelity of relative dynamics these models become very complicated to implement. That is why the HCW equations remain extremely popular after all these developments. However, their simplicity causes issues when there is In-Track separation between the Chief and Deputy satellites. The error in the dynamics increases as this separation increases which leads to a typical constraint that the separation between the Chief and Deputy needs to be much smaller than the radius of the Chief's orbit. That is where this works starts, by examining into ways to increase the accuracy in the HCW equations as the In-Track separation between the Chief and Deputy grows. In which, this will be done by using a curvilinear coordinate system. Furthermore, a technique of using a Virtual Chief satellite will by employed to allow for the HCW equations to be valid for cases where the Chief is in an eccentric orbit. / Master of Science / There are many different models that are used to model the relative motion between two satellites. These models vary from low to high fidelity in the different types of perturbation and ranges that they can model. These higher fidelity models because very complex to implement and while useful the low fidelity models are still popular, specifically the HCW equations. This thesis works on making the HCW equations valid for a larger range of cases.

Traditionally the role of a Chapel is to offer society a place to worship, find solitude, sanctuary, spiritual enlightenment, religious fulfillment, and its inspiration. In an effort to reinforce and accentuate these experiences, this project explores the architectural concepts of procession, transition, and materiality of a Chapel. / Master of Architecture

Based on experimentation with the steam bending of wood to curved shapes, this thesis describes my involvement with three basic aspects of the process. First is the procurement, assimilation, and construction of the equipment and apparatus necessary for the steam bending of wood. Secondly, the determination of certain qualities of particular woods in reference to steam bending is made. This includes: woods easily bent; woods not easily bent; the time required to plasticize stock; and the time required to set curves. Also noted are some of the physical limitations involved in bending stock with steam in the craftsman's studio. Thirdly, steam bent wood is related to furniture design in terms of the craftsman's approach to the design and to the problems inherent in this process.

My thesis work is about flow. Indeterminate lines symbolize the developing plant form and explore the perception of space by experimenting with the subject's proportion and shape. Movement is also a vital factor of space, a notion found in the early forms of cursive script (grass script) of Far Eastern calligraphy. My individual plant pieces work as dots and lines of cursive script. An installation's ceramic pieces illustrate similar flow and movement when viewed as a whole.

[pt] No presente trabalho é realizada uma análise do desempenho de três diferentes modelos de turbulência na previsão de escoamentos que apresentam separação e recolamento. Investigou-se o escoamento turbulento através de dutos com obstruções curvilíneas. Os modelos selecionados pertencem a classe de modelos de duas equações diferenciais k-e para baixos números de Reynolds. A análise tem por objetivo verificar se estes modelos são capazes de captar as regiões de recirculação e recuperação de pressão após a obstrução, grandezas fundamentais para a avaliação da distribuição de tensões. Os campos de velocidade, energia cinética turbulenta, taxa de dissipação obtidos pelos diferentes modelos são comparados com dados numéricos e experimentais na literatura, visando identificar qual é o modelo mais adequado para esse tipo de escoamento. Para a determinação numérica do escoamento na geometria com uma obstrução curvilínea, do tipo cossenoidal, utilizou-se o método de volumes finitos com coordenadas curvilíneas não ortogonais que se adaptam à geometria. Os componentes contravariantes da velocidade foram empregadas como variáveis independentes nas equações de conservação de quantidade de movimento e o acoplamento velocidade pressão foi resolvido pelo algoritmo SIMPLEC. Dentre os modelos testados, nenhum conseguiu reproduzir exatamente todos os dados experimentais, porém concluiu-se que o modelo LSH, proposto por Launder e Sharma (1974) com a modificação proposta por Hanjalic e Launder (1980) apresentou o melhor desempenho, o qual pode ser considerado como satisfatório. / [en] In the present work an analysis of the performance of three different turbulence models in the prediction of flows that present separation and reattachment. The turbulent flow was investigated through ducts with curvilinear obstructions. The selected models belong to the class of models with two differential equations k-e for low numbers of Reynolds. The objective of the analysis is to verify if these models are capable of capturing the recirculation areas and pressure recovery after the obstruction, fundamentals for the evaluation of the distribution of tensions. The fields of velocity, turbulent kinetic energy, dissipation rate obtained by the different models are compared with numeric and experiments data found in the literature, seeking to identify which is the model more adapted for those type of flows. The numeric determination of the fluid flows in the geometry with a curvilinear obstruction, described by a sine curve, was accomplished by a finite volume method with non orthogonal curvilinear coordinates which adapt to the geometry. The countervariants velocity components was employed as independent variables in the momentum conservation equation and the velocity-pressure coupling was solved by the SIMPLEC algorithm . Among all the tested models, none was able to reproduce exactly the experimental data. However, the LSH model, proposed by Launder and Sharma (1974) with the modification proposal for Hanjalic and Launder (1980) presented the best performance, which can be considered satisfactory. / [es] En el presente trabajo se analiza el desempeño de tres modelos de turbulencia diferentes para la previsión de flujos con separación y readherencia. Se investigó el flujo turbulento a través de conductos con obstrucciones curvilíneas. Los modelos seleccionados pertenecen a la clase de modelos de dos ecuaciones diferenciales k-y para bajos números de Reynolds. El análisis tiene como objetivo verificar si estos modelos son capaces de captar regiones de recirculación y recuperación de presión después de la obstrucción, cantidades fundamentales para la evaluación de la distribución de tensiones. Se comparan los campos de velocidad, energía cinética turbulenta, tasa de disipación obtenidos por los diferentes modelos con los datos numéricos y experimentales en la literatura, identificando cuál es el modelo más adecuado para ese tipo de flujo. Para la determinación numérica del flujo en la geometría con una obstrucción curvilínea, del tipo cosenoidal, se utilizó el método de volúmenes finitos con coordenadas curvilíneas no ortogonales que se adaptan a la geometría. Los componentes contravariantes de la velocidad fueron utilizados como variables independentes en las ecuaciones de conservación de movimiento y el acoplamiento velocidad-presión fue resuelto a través del algoritmo SIMPLEC. Ninguno de modelos provados consiguió reproducir exactamente todos los datos experimentales, mas se puede concluir que el modelo LSH, propuesto por Launder y Sharma (1974) con la modificación propuesta por Hanjalic y Launder (1980) presentó el mejor desempeño, que puede ser considerado como satisfactorio.

Hydraulic structures such as dykes and groynes are commonly used to help control river flows and reduce flood risk. The present research aims to develop an idealized model of the hydrodynamics in the vicinity of a large river bend, and the advection and mixing processes where groynes are located. In this study a curvilinear model of shallow water equations is applied to investigate chaotic advection of particles in a river bend similar in dimensions to a typical bend in the River Danube, Hungary. First, a curvilinear grid generator is developed based on Poisson-type elliptic partial differential equations. The grid generator is verified for benchmark tests concerning a circular domain and for distorted grids in a rectangular domain. It is found that multi-grid (MG) and conjugate gradient (CG) methods performed better computationally than successive over-relaxation (SOR) in generating the curvilinear grids. The open channel hydrodynamics are modelled using the shallow water equations (SWEs) derived by depth-averaging the continuity and Navier-Stokes momentum equations. Both Cartesian and curvilinear forms of the shallow water equations are presented. Both sets of equations are discretized spatially using finite differences and the solution marched forward in time using fourth-order Runge-Kutta scheme. The shallow water solvers are verified and validated for uniform flow in the rectangular channel, wind-induced set up in rectangular and circular basins, flow past a sidewall expansion, and Shallow flow in a rectangular channel with single groyne. A Lagrangian particle tracking model is used to predict the trajectories of tracer particles, and bilinear interpolation is used to provide a representation of the continuous flow field from discrete results. The particle tracking model is verified for trajectories in the flow field of a single free vortex and in the alternating flow field of a pair of blinking vortices. Excellent agreement is obtained with analytical solutions, previously published results in the literature. The combined shallow flow and Lagrangian particle tracking model is then used to simulate particle advection in the flow past a side-wall cavity containing a groyne and reasonable agreement is obtained with published experimental and alternative numerical data. Finally, the combined model is applied to simulate the shallow flow hydrodynamics, advection and mixing processes in the vicinity of groynes in river bend, the dimensions representative of a typical bend in the Danube River, Hungary.

Architectural curvilinear form has been on the scene since the time of the first building shelters. Curve is the most common form in nature. This phenomenon inspired human beings while they are building structures. Curvilinear form has developed over centuries, via structural enhancements and aesthetic tenets. A symbolic meaning is tailored to curvilinear structures such as use of domes in religious buildings. However, the difficulties in the construction process of these forms have been a challenge for people throughout the history. Today, introduction of computer aided design and manufacturing technologies into building industry encourages the use of curvilinear forms in architecture. This study intends to explore the relationship between structure and architectural curvilinear form. The curvilinear form will be examined basically according to its structural potentials through its geometrical configuration. A computer model of the roof of Channel Tunnel Railway Terminal at Waterloo is generated and with some geometrical modifications for the configuration of the roof, new schemes of structures are obtained. An analytical comparison of structural behavior and efficiency is made via the computer model of the roof and these modified configurations.

The present study considers steady laminar two-dimensional incompressible flow over both in-line and staggered flat tube bundles used in heat exchanger applications. The effects of various independent parameters, such as Reynolds number (Re), Prandtl number (Pr), length ratio (L/Da), and height ratio (H/Da), on the pressure drop and heat transfer were studied. A finite volume based FORTRAN code was developed to solve the governing equations. The scalar and velocity variables were stored at staggered grid locations. Scalar variables (pressure and temperature) and all thermophysical properties were stored at the main grid location and velocities were stored at the control volume faces. The solution to a one-dimensional convection diffusion equation was represented by the power law. The locations of grid points were generated by the algebraic grid generation technique. The curvilinear velocity and pressure fields were linked by the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm. The line-by-line method, which is a combination of the Tri-Diagonal Matrix Algorithm (TDMA) and the Gauss-Seidel procedure, was used to solve the resulting set of discretization equations. The result of the study established that the flow is observed to attain a periodically fully developed profile downstream of the fourth module. The strength increases and the size of the recirculation gets larger as the Reynolds number increases. As the height ratio increases, the strength and size of the recirculation decreases because the flow has enough space to expand through the tube passages. The increase in length ratio does not significantly impact the strength and size of the recirculation. The non-dimesionalized pressure drop monotonically decreased with an increase in the Reynolds number. In general, the module average Nusselt number increases with an increase in the Reynolds number. The results at Pr = 7.0 indicate a significant increase in the computed module average Nusselt number when compared to those for Pr = 0.7. The overall performance of in-line configuration for lower height ratio (H/Da = 2) and higher length ratio (L/Da = 6) is preferable since it provides higher heat transfer rate for all Reynolds numbers except for the lowest Re value of 25. As expected the staggered configurations perform better than the in-line configuration from the heat transfer point of view.

A review of the literature indicates that a universally enhancing relationship between market orientation and performance is not conclusively supported. Recent research suggests that the relationship between marketing investments and profit may be inverted U-shaped such that there is an optimal level of marketing investments which maximises profit (Mantrala et al 2007). In this study, it is proposed that market orientation has different curvilinear relationships with different types of performance. Using a performance categorisation suggested by Kirca et al (2005), it is theorised that market orientation s relationship with revenue-based performance (e.g. sales growth, market share growth) is subject to diminishing returns such that performance is enhanced for all levels of market orientation but the incremental benefits diminish as market orientation increases. For cost-based performance (e.g. profit, return on sales), it is proposed that the incremental costs of implementing market oriented activities may exceed the benefits. Thus, cost-based performance may have an inverted U-shaped relationship with market orientation. Three mechanisms by which diminishing returns affect the market orientation - performance relationship are identified; duplication, contradiction and prioritisation. A review of over 400 papers in the market orientation literature demonstrates that a research gap exists for different curvilinear relationships between market orientation and different types of performance. In particular, an inverted U-shaped relationship has not previously been found between market orientation and profit. A sampling frame was selected to control for both the macro-environment, and different performance levels in different industries (Dess and Robinson 1984). In a sample of 113 UK car dealers operating in the new car market the hypothesised relationships were tested using both objective and subjective performance measures. The findings relating to objective performance measures support the full inverted U-shaped relationship between market orientation and profit across the observed range of values. The relationship for objective revenue-based performance is more curvilinear with significant linear and curvilinear components. In highly competitive environments maximum profit shifts to a higher level of market orientation and overall the relationship is predominantly enhancing. Conversely, in uncompetitive environments profit is maximised at a lower level of market orientation and the relationship becomes detrimental at moderate market orientation levels. In recession, the profit for all new car dealers is reduced and maximum profit occurs at a lower market orientation level. In addition, the relationship between market orientation and sales growth turns negative in a recession. Interestingly, the results for subjective performance are distinctly different to, and sometimes contradict, the objective performance results. In particular, subjective performance predominantly has a positive linear relationship with market orientation.

abstract: When a rolling ball exits a spiral tube, it typically maintains its final inertial state and travels along straight line in concordance with Newton's first law of motion. Yet, most people predict that the ball will curve, a "naive physics" misconception called the curvilinear impetus (CI) bias. In the current paper, we explore the ecological hypothesis that the CI bias arises from overgeneralization of correct motion of biological agents. Previous research has established that humans curve when exiting a spiral maze, and college students believe this motion is the same for balls and humans. The current paper consists of two follow up experiments. The first experiment tested the exiting behavior of rodents from a spiral rat maze. Though there were weaknesses in design and procedures of the maze, the findings support that rats do not behave like humans who exhibit the CI bias when exiting a spiral maze. These results are consistent with the CI bias being an overgeneralization of human motion, rather than generic biological motion. The second experiment tested physics teachers on their conception of how a humans and balls behave when exiting a spiral tube. Teachers demonstrated correct knowledge of the straight trajectory of a ball, but generalized the ball's behavior to human motion. Thus physics teachers exhibit the opposite bias from college students and presume that all motion is like inanimate motion. This evidence supports that this type of naive physics inertial bias is at least partly due to participants overgeneralizing both inanimate and animate motion to be the same, perhaps in an effort to minimize cognitive reference memory load. In short, physics training appears not to eliminate the bias, but rather to simply shift it from the presumption of stereotypical animate to stereotypical inanimate behavior. / Dissertation/Thesis / M.A. Psychology 2013